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On the Accuracy of the Semiclassical Trace Formula

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Harel Primack, Uzy Smilansky

chao-dyn · Submitted 16 Jan 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality.

how it is stated · hedged possibility 0.83 read the record →

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arXiv IDchao-dyn/9801025 (version 2)
Pith IDHHKTTX76, Pith's permanent record of this paper and its review
CitationHarel Primack, Uzy Smilansky. "On the Accuracy of the Semiclassical Trace Formula." arXiv:chao-dyn/9801025 (1998). https://pith.science/paper/HHKTTX76
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,379 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.70 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. background 1.00 0.04 0.02 asserted 1.00
s1 When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. background 0.98 0.05 0.04 hedged possibility 0.64
s2 If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. background 0.71 0.04 0.03 hedged possibility 0.66
s3 In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. contribution 0.99 0.85 0.80 hedged possibility 0.83
s4 Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments. method 0.57 0.96 0.09 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.53 · evidence from simulation or computation 1.00.

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments.

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